Learn Croatian: Orkestar uvijek svira s oduševljenjem i sa zadovoljstvom. - The orchestra always plays with enthusiasm and with pleasure.

The preposition is normally just s. However, it changes to sa when the following word starts with a sibilant consonant like s, š, z, or ž, because it would be too hard to pronounce otherwise. Since zadovoljstvom starts with a z, it gets sa.

Why do we need the preposition s/sa here? I thought the Instrumental case could mean 'with' all by itself.

You use the Instrumental case without a preposition when talking about a physical tool, like writing with a pen. But when you are talking about an abstract feeling or the manner in which you do something, like playing with enthusiasm, you must include the preposition s or sa before the Instrumental noun.

What are the base forms of oduševljenjem and zadovoljstvom, and why do they have different endings here?

The base forms are oduševljenje (enthusiasm) and zadovoljstvo (pleasure). Both are neuter nouns. In the Instrumental case, neuter nouns take the ending -om, but if the base noun's stem ends in a 'soft' consonant sound like the nj in oduševljenje, the ending becomes -em. That is why we get oduševljenjem and zadovoljstvom.

Could I use the verb svira if this sentence was about a sports team playing with enthusiasm?